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VIII
<br />TA13LE II. - Radii, Ordinates and Deflections. • Chord =100 ft.
<br />Deg.'
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Der.
<br />Dist.
<br />Der.
<br />1fnr
<br />Deo.
<br />Radius
<br />Mid.
<br />Ord
<br />Tan.
<br />Dist,
<br />lief.
<br />Dist.
<br />Def.
<br />j or
<br />Pta
<br />2° 17
<br />ft.
<br />ft.
<br />ft.
<br />ft.
<br />r
<br />1° 59
<br />ft,
<br />ft.
<br />ft,
<br />ft.
<br />I
<br />0°10'
<br />34377.
<br />.03G
<br />.145
<br />.291
<br />0.05'
<br />7°
<br />819.0
<br />1.525
<br />6.105
<br />L?.21
<br />2.10
<br />20
<br />17159.
<br />.073
<br />.291
<br />.5S2
<br />0.10
<br />20'
<br />751.8
<br />1.600
<br />G..i95
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />109
<br />.43G
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.03
<br />2.25
<br />40
<br />5594.4
<br />.145
<br />.582
<br />1.164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2.30
<br />50
<br />6575.5
<br />.152
<br />. 727
<br />.1.454
<br />0.25
<br />8
<br />716.5
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />'.873
<br />1.745
<br />0.30
<br />20
<br />GS8.2
<br />1.819
<br />7.266
<br />1.1.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />3.018
<br />2.03G
<br />0.35
<br />30
<br />G74.7.
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />-4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />GG1.7
<br />1.892
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9
<br />G37.3
<br />1.965
<br />7.840
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />:364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2.037
<br />8.136
<br />16.27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />G03.8
<br />2.07.1
<br />8.281
<br />10.56
<br />2.55
<br />2
<br />2564.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.4731.891
<br />3.751
<br />0.65
<br />10
<br />';73.7
<br />2.10
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />.2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />18.30
<br />3'.15
<br />30
<br />2292.0
<br />.545
<br />2.151
<br />4.303
<br />0:75
<br />11
<br />.521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.5S2
<br />2.327
<br />4.654
<br />O.SO
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.:618
<br />2.472
<br />4.045
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />3
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3'2.730
<br />10.59
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />4.11.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />.5.817
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />3.054
<br />6.105
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />G.393
<br />1.10
<br />30
<br />396.2
<br />3.163
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />,1495.0
<br />.836
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />333.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />A
<br />1432.7
<br />'.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.357
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.25,
<br />16
<br />359.3
<br />3.406
<br />13.92
<br />27. S4
<br />4.50
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />25.70
<br />4.95
<br />30
<br />1273.6
<br />.952
<br />3.926
<br />7.552
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />40
<br />1228.1
<br />1.01S
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />51146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />257.9
<br />4.374
<br />17.37
<br />34.73
<br />G.00
<br />10
<br />1109.3
<br />1.127
<br />4.501
<br />.9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />36.44
<br />6.30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />9.305
<br />1.60
<br />22
<br />262.0
<br />4.514
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.57
<br />0.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.50
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088
<br />10.15
<br />1.75
<br />25
<br />231.0
<br />5.47621.64
<br />43.28
<br />7.50
<br />6''
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.50
<br />'LG.
<br />222.3
<br />5.697
<br />22.50
<br />44.9.
<br />7.SO
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.S5
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />8:10
<br />20
<br />005.1
<br />1.382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />200.7'6.139
<br />24.19
<br />4S.3S
<br />5.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />5.70
<br />40 1
<br />859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.58
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of lel:gth (C) is equal to .0012 C''
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fita 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Clave
<br />Radius
<br />50
<br />31/2 sub chord sin of : def. angle
<br />n
<br />Length
<br />of arc
<br />for IOU,
<br />sin.',def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft. -
<br />30°
<br />193.18
<br />1° 51,
<br />2° 17
<br />2- 58,
<br />T 3°43'
<br />101.15
<br />32°
<br />181.39
<br />1° 59
<br />2° 25'
<br />3°.10'
<br />3° 58`
<br />1or.J3
<br />34°
<br />171. of
<br />2° 06'
<br />2° 33'
<br />3° z1'
<br />r ° I2'
<br />I01.48
<br />°
<br />36
<br />i61.8o
<br />2° 13'
<br />2° 41'
<br />3° 30'
<br />4° 26'
<br />iof.66
<br />38°
<br />153.58
<br />2°.20 '
<br />2° =l9'
<br />3° 441
<br />4° 40'
<br />I0I.85
<br />40°
<br />146.19
<br />2° 27`
<br />2° 57'
<br />30 5j
<br />:}° J4'
<br />102.06
<br />42°
<br />139.52 "
<br />2° 34'
<br />3 05'
<br />4° 07'
<br />5° 08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />30,-1
<br />4° 18'
<br />1 5° 22'
<br />102.:43
<br />460
<br />'127-97
<br />2° 48'
<br />3°. 21'
<br />4° 29'
<br />' 5° 36'
<br />102.76
<br />4So
<br />12_.92
<br />2° 53,
<br />3° 20'
<br />4° 40'
<br />5° 5()/
<br />163. o0
<br />50
<br />118.31
<br />�° a_'
<br />3° 38'
<br />4° 51'
<br />6° 04
<br />103.24
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46,
<br />5° 02'
<br />60 17
<br />103.54
<br />54'
<br />110.11
<br />3°16
<br />3°54
<br />5°'13'
<br />6°31'
<br />103.84
<br />56°
<br />1o6.5o
<br />3° 22'
<br />4° oz'
<br />S°
<br />60 44'
<br />104.14
<br />58°
<br />103.14
<br />.3' 229'
<br />4° Ici
<br />5° 34'
<br />6° 57'
<br />I04.43
<br />6o°
<br />foo.00
<br />3°35'
<br />4°1S'
<br />5°4427
<br />7°If'
<br />104-72
<br />IX
<br />CURVE FORMULAS
<br />T= R tan 3 I R= T cot. 1 I Chord def. = chord2
<br />r _ 5o tan I
<br />_JD R = 50
<br />Sin. I D = �o Sin. a D ' No. chords = I
<br />R E= R ex. sec I D
<br />Sin.'} D = 56 tan -.1I E = T tan I -Tan. def. _ chord def.
<br />The square of any distance,, divided by twice the 'radius, will equal
<br />the distance from tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply the given distance by .01745 (def. for I° for i ft."
<br />see Table'IL), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Rase loo, Alt. 10.IO'-_200=.5. loo+.5=Ioo.5 hyp.
<br />Given Hyp.Ioo,Alt. 25.252=200=3.125.100-3.125=96.875=Base.
<br />Error in first example, .002; In last, .045.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by i i, and divide by 7.
<br />LEvEhING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574 da, where d is the distance in miles.
<br />The correction for curvature alone is closely, ;de. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, de, d;,, etc. are the discrepancies of various
<br />result3 from the mean, and if fid==the sum of the squares of these differ-
<br />ences and r.=the number of observations, then the probable error of the
<br />mean= oda
<br />± 0.6745.
<br />11 (n-1)
<br />SOLAR ErrimiFizis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3;x5l, in., with about 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directions and tables for determining the meridian
<br />and the latitude from observations on, the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - Minutes in Decimals of a Deuce.
<br />P
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41' .6833
<br />51'
<br />.8500 '
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />..5333
<br />42 .7000
<br />52
<br />.8667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.31333
<br />0, 3'
<br />.5500
<br />43 .7167
<br />53
<br />•8533
<br />4
<br />.0667
<br />14:
<br />.2333
<br />21:
<br />.4000
<br />3.4
<br />. SGG7
<br />44 .7333
<br />54
<br />' :9000
<br />5
<br />OSI -13
<br />15
<br />.2500
<br />25
<br />!-167
<br />35
<br />.5333
<br />45 .7600
<br />55
<br />'.9167
<br />G
<br />.1060
<br />1G
<br />.2S67
<br />26
<br />:333
<br />3G
<br />.6000
<br />4G .7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2533
<br />27
<br />.4500
<br />37
<br />.6167
<br />47 .7533
<br />57
<br />.9500
<br />8
<br />.1333
<br />15
<br />.3000
<br />28
<br />.5667
<br />38
<br />.6333
<br />48 -000
<br />,5S
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />'T9
<br />.4833
<br />39
<br />.6500
<br />49 .3167
<br />59
<br />.9S33
<br />10
<br />.1661 11
<br />20
<br />1 .3333
<br />1130
<br />1 .5000
<br />11 40
<br />1 .G667 1150
<br />1 .5313',J
<br />GO
<br />11.0000
<br />TABLE V. - Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />%
<br />3-1G
<br />/.y
<br />5-1G
<br />;�.W73'13
<br />.003^_
<br />0078
<br />.0104
<br />.0156.
<br />.0208
<br />.0260
<br />.03.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G
<br />.0333,
<br />.1667
<br />.3500
<br />.3333
<br />.4167
<br />.5000
<br />.'5.91.67
<br />
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